Many of the houses in this area were built in the first half of the 19th century, following the enlargement of the nearby Riverdale Mill, one of many on the Ravensbourne.

Avenue Square was typical of the tiny houses built between the High Street and the Ravensbourne river.

The houses were demolished after damage sustained in the late 1930s and the whole area was swept away when Molesworth Street was promoted as a by-pass for the High Street in the mid 1990s.